Fluctuations and instabilities of model amphiphile interfaces

We study the stability of planar, cylindrical and spherical interfaces with respect to shape and width fluctuations for a model amphiphile solution de scribed by a free energy density functional with square-gradient and square -laplacian terms. That is, we determine the stability matrix when the stati onary state consists of an interface with given geometry that separates two immiscible solvent phases. From the spectrum and the related eigenfunction s of, this matrix we establish where lamellar and micellar domain-structure d phases occur, and contrast our results with those for a simple square-gra dient fluid model for which these: phases are always unstable. We also char acterize some instability properties such as the buckling of lamella, the u ndulation of cylindrical structures and the nucleation of micelles. (C) 200 1 Elsevier Science B.V. All rights reserved.